algebra 1 pap name period - colleyville heritage high school
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Algebra1PAP Name______________Period____
Unit8NotesandAssignmentsNotesandAssignmentPacket:Youwillbegivenapacketatthebeginningofeachunit.YouwillonlyreceiveONEcopyofthisandyouareresponsibletokeeptrackofit.Ifyoumisplaceit,youmustprintyourownfromGoogleClassroom.UnitAgenda:Youwillalsoreceiveacoloredunitagendaforeachpacket.Thisfirstdayoftheunit,youshouldlookovertheobjectivesandcreateagoalforyourselfthatyouwishtoaccomplish.Aseachobjectiveistaught,youshouldrateyourselfandidentifyagrowthopportunity.Thiscanbedoneinclassorathome.Afterwedotestcorrections,youaretocompletetheunitreflection.Homework/Assignments:Youmuststayontopofyourassignments.Thesewillbechecked(canhappenunannounced)thedayaftertheyareassigned,thedayofthequiz,orthedayofthetest.Youshouldbepreparedeitherway!Itisyourresponsibilitytogiveyourselfandaccuracygradeforeachassignment.Ontestday,youwillbeexpectedtoturninacompletedagenda,packet,andtestreview.AbsentWork:Ifyouareabsent,itisyourresponsibilitytowatchthevideoandcompletethemissingnotes.STAARPractice:Attheendofeachunitpacket,thereisaSTAARpractice.Thesequestionsmustbecompletedbythatunit’sreviewday.
Unit8Outline:SolvingQuadratics8-1Notes:SolvebyFactoring8-1WS:SolvebyFactoring8-2Notes:SolvebySquareRootMethod8-2WS:SolvebySquareRootMethod8-3Notes:SolvebyCompletetheSquare8-3WS:SolvebyCompletetheSquare8-4Notes:SolvebyQuadraticFormula8-4WS:SolvebyQuadraticFormula8-5Notes:SolveusingAllMethods8-5WS:SolveusingAllMethods8-1–8-5Quiz8-6Notes:QuadraticApplications8-6WS:QuadraticApplicationsUnit8STAARReviewUnit8ReviewUnit8Test
2/20/20
1
Factor and Solve
Solve the following.2x – 1= 0
Solve the following.(x + 3) (2x – 1) = 0
Solve the following.(x – 5) (3x + 2) = 0
Solve the following.x (2x + 7) = 0
Factor and Solve.
x2 + 6x + 8 = 0
8-1 Noteshttps://youtu.be/ouxEPWM9iEU
2/20/20
2
Factor and Solve.
2x2 – 5x – 7= 0Factor and Solve
10x2 = –10x
Factor and Solvex2 – 3x = 28
You try!1. 5x2 = 25x 2. x2 – 11x = –18
8-1 Notes
https://youtu.be/ouxEPWM9iEU
Worksheet Solving by Factoring Name _________________________
Solve the quadratics by factoring.
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12. –
8-1 WS
13. 14.
15. 16.
17. 18.
19. 20.
21. 22.
23. 24.
25.
8-1 WS
8-2Notes Name________________
SimplifyingRadicals
1. 75 2. 200 3. 48 4. 40 5.3 72 6.-4 243
7.100)* 8.8
)*
SolvebyusingtheSquareRootMethod.
1. x2=81 2.x2=50 3.m2+5=1054.m2-9=31 5.3m2=3 6.2m2+1=19
7.4m2–5=75
https://youtu.be/kDm5dYETrdw
https://youtu.be/fJsPoTJbuBE
SquareRootMethodWS Name______________________
Simplifyeachsquareroot.1. 96 2. 2163. 98 4.3 185. 72 6. 1447.2 45 8. 1759. 343 10. 12
8-2 WS
SquareRootMethodWS Name______________________
Solveeachequationbytakingsquareroots.Makesureyousimplifyyouranswer.11.*+ = 76 12.*+ = 1613.-+ = 21 14..+ = 415.-+ + 8 = 28 16.−61+ = −41417.-+ − 5 = 73 18.72+ + 1 = 2919.21+ + 10 = 210 20.104+ − 10 = 470
8-2 WS
2/21/20
1
SolveusingCompletetheSquare
x2 +2x– 35=0SolveusingCompletetheSquare
x2 - 2x– 15=0
SolveusingCompletetheSquare
x2 +4x=3SolveusingCompletetheSquare
x2 - 8x=-7
SolveusingCompletetheSquare
2x2 - 4x– 14=0SolveusingCompletetheSquare
5x2 +20x+10=-5
Complete the Square
https://youtu.be/fu4qSmlIQFg
8-3 Notes
Complete(the(Square(WS( ( Name____________________________(
Solve(the(equation(by(competing(the(square.((1.(x2(+(2x(–(63(=(0(( ( ( ( ( 2.(m2(–(8m(–(48(=(0((((((((3.(r2(+(2r(–(48(=(–((6((( ( ( ( ( 4.(x2(–(2x(–(8(=(0((((((((5.(n2(+(16n(–(22(=(0( ( ( ( ( 6.(k2(+(2k(–(33(=(0((((((((7.(x2(–(12x(+(26(=(0( ( ( ( ( 8.(b2(+(2b(–(3(=(0((((((((9.(m2(–(2m(–(48(=(0( ( ( ( ( 10.(x2(+(8x(+(12(=(0(((((
8-3 WS
Complete(the(Square(WS( ( Name____________________________(
11.(r2(–(8r(+(21(=(6( ( ( ( ( 12.(x2(+(12x(+(20(=(0((((((((13.(x2(–(2x(=(3( ( ( ( ( ( 14.(k2(+(10k(+(14(=(–(7((((((((15.(7b2(–(14b(–(56(=(0( ( ( ( ( 16.(2x2(+(12x(+(10(=(0((((((((17.(m2(+(18x(=(–(36( ( ( ( ( 18.(r2(+(10r(=(23(((((((((19.(5x2(–(10(=(10v(( ( ( ( ( 20.(4x2(+(16x(=(64((
8-3 WS
2/20/20
1
ìSolve Quadratic EquationsQuadraticFormula
What is a, b, and c?
x2 + 3x −12 = 0
Solve using Quadratic Formula
4x2 +11x − 20 = 0
Solve using Quadratic Formula
x2 − 5x − 24 = 0
Solve using Quadratic Formula
4x2 + 7x −15 = 0
Solve using Quadratic Formula
2x2 + 39 = −18x
8-4 Notes
https://youtu.be/JhGb7LhaQjI
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Using the Quadratic Formula
Solve each equation with the quadratic formula.
1)
m2 − 5
m − 14 = 0 2)
b2 − 4
b + 4 = 0
3)
2
m2 + 2
m − 12 = 0 4)
2
x2 − 3
x − 5 = 0
5)
x2 + 4
x + 3 = 0 6)
2
x2 + 3
x − 20 = 0
7)
4
b2 + 8
b + 7 = 4 8)
2
m2 − 7
m − 13 = −10
-1-
e8-4 WS
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9)
2
x2 − 3
x − 15 = 5 10)
x2 + 2
x − 1 = 2
11)
2
k2 + 9
k = −7 12) 5
r2 = 80
13)
2
x2 − 36 =
x 14)
5
x2 + 9
x = −4
15)
k2 − 31 − 2
k =
−6 − 3
k2 − 2
k 16) 9
n2 =
4 + 7
n
17)
8
n2 + 4
n − 16 = −
n2 18)
8
n2 + 7
n − 15 = −7
-2-
8-4 WS
Solve&Quadratic&Equations&Using&Any&Method& Name_________________________&
Solve&by&Graphing&f(x)&=&x2&–&4&&&&&&&&&&&
Factoring&x2&–&4&=&0&
Square&Root&Method&x2&–&4&=&0&&&&&&&&
Quadratic&Formula&f(x)&=&x2&–&4&&
Complete&the&Square*&x2&–&4&=&0&&&&&&&&&&
Types&of&Solutions&1&Solution:&&&&&2&Solutions:&&&&No&Solution:&&
*Typically,&you&would¬&use&Complete&the&square&when&b&=&0.&This&was&just&to&show&that&all&methods&lead&to&the&same&answers.&
8-5 Notes https://youtu.be/EgVLA35nsck
Name: __________________________________ Date: __________________________
Practice : Quadratics
Solve the quadratic equation using any method. Round your solutions to the nearest hundredth, if necessary. Write which method you chose to use for each problem. 1. 6x² - 216 = 0 2. 8x² = 56 3. 5x² - 10x = 0 4. x² + 8x + 7 = 0 5. x² - 6x + 1 = 0 6. -9x² + 10x = 5 7. -10x² = -50 8. x² - 16x = -64 9. x² + 3x - 8 = 0 10. x² = 14x – 49 11. x² + 6x = 14 12. -5x² + x = 13
8-5 WS
name______________________________________& & & & & date________________________________&
Unit&8:&Notes&Quadratic&Equation&Applications&
Write&an&equation&and&solve&the&following.&&Be&sure&to&identify&your&unknowns.&
1.& If&a&number&is&subtracted&from&its&square&the&result&is&12.&&Find&the&number.&
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2.& Twice&a&number&is&63&less&than&its&square.&&Find&the&number.&
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3.&&& A&negative&number&is&thirty&less&than&its&square.&&Find&the&number.&
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4.&&& The&square&of&a&number&increased&by&17×&the&number&is&M72.&&Find&the&number.&
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5.& Two&consecutive&negative&even&integers&have&a&product&of&624.&&Find&the&numbers.&
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8-6 Notes. https://youtu.be/lDWZZroeAko
6.&& The&length&of&a&rectangle&is&8&cm&greater&than&twice&its&width.&&Find&the&dimensions&of&the&rectangle&if&its&area&is&42&cm2.&&What&is&the&perimeter?&
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7.& Use&the&formula&h"="rt"–"16t2&where&h&is&height&in&feet,&t&is&time&and&r&is&rate&or&velocity&&to&determine&when&a&potato&will&be&24&feet&high&if&it&is&shot&off&the&ground&from&a&potato&gun&with&an&initial&speed&of&40&ft/sec.&&&
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8.&& A&painter&drops&his&paint&brush&from&a&400&foot&building.&&Use&the&vertical&motion&model&(vmm)&to&write&an&equation&that&models&this&situation.&&Use&your&equation&to&find&the&height&of&the&paint&brush&after&4&seconds?&
&(vmm)&h&=&M16t²&+&vt&+&s&&&&h&is&height,&v&is&vertical&force,&s&is&initial&height.&&&
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& When&is&the&paint&brush&still&256&feet&from&the&ground?&
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https://youtu.be/lDWZZroeAko8-6 Notes
Name______________________________________&& & & & & date_________________________&
Unit&8:&Quadratic&Equation&Application&Practice&
Write&an&equation&and&solve&the&following.&&Make&sure&you&identify&your&unknowns.&
1.& If&a&number&is&subtracted&from&its&square&the&result&is&72.&&Find&the&number.&
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2.&&& A&negative&number&is&42&less&than&its&square.&&&Find&the&number.&
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3.&&& Two&consecutive&negative&odd&integers&have&a&product&of&143.&&Find&the&numbers&
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4.&& The&length&of&a&rectangle&is&six¢imeters&less&than&twice&its&width.&&Find&the&dimensions&of&the&rectangle&if&its&area&is&108&cm2.&&&
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5.& The&length&of&a&rectangle&is&eight¢imeters&greater&than&its&width.&&Find&the&dimensions&of&the&rectangle&if&its&area&is&240&cm2.&
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6.& Find&two&consecutive&positive&odd&integers&whose&product&is&195.&
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8-6 WS
7.& One&side&of&a&rectangular&patio&is&5&feet&longer&than&an&adjacent&side.&&If&the&area&of&the&patio&is&104&square&feet,&how&long&is&the&longer&side?&
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8.& A&golf&ball&is&hit&upward&with&an&initial&speed&of&24.5&meters/sec.&&Using&the&formula&h"="rt"–"4.9t2&where&h&is&height&in&meters,&r&is&rate&or&velocity,&and&t&is&time&in&seconds&determine&when&the&ball&is&19.6&meters&high.&
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9.& &A&model&rocket&is&fired&upward&from&the&ground&with&an&initial&velocity&of&160&feet/sec.&&Using&the&formula&h"="rt"–"16t2&where&h&is&height&in&feet,&r&is&rate&or&velocity,&and&t$is&time&in&seconds&determine&when&the&rocket&is&400&feet&high.&
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8-6 WS
Unit8STAARPractice Name________________________
Unit8STAARPractice Name________________________
Unit8Review Name__________________
Simplifythesquareroots.1. 81 2. 75 3. 98 Solvebyusingsquareroots.4.3x2–27=0 5.–7x2=–56 6.9x2–235=206Findtheexactsolutionforeachequationbycompletingthesquare.7.x2–2x–48=08.x2–14x+19=09.3x2+24x=15Solvebyfactoring.10.6x2–2x=0 11.x2+3x=54 12.3x2–4=–x
Unit8Review Name__________________
Solveusingthequadraticformula.13. 14 2 =x 14. 3m2 − 4 = 11m 15. r2 −10r = −22 Solveusinganymethod.16. x2 + 8x +15 = 0 17. x2 = 16 18.2x2–x–36=019.Whataretherootstothefunction? 20.Findthex-interceptsofthefunction. Howmanyrootsdothefollowingequationshave?21. 72 += xy 22. 962 ++= xxy 23. 542 --= xxy
Unit8Review Name__________________
24.Arocketislaunchedfromatopa38-footcliffwithaninitialverticalvelocityof125feetpersecond.Theheightoftherockettsecondsafterlaunchisgivenbytheequationh = −16t 2 +125t + 38 .Howlongaftertherocketislaunchedwillithittheground?Roundyouranswertothenearesttenthofasecond.25.Ifanumberissubtractedfromitssquaretheresultis56.Findthenumber.26.Thelengthofarectangleis5cmlongerthanthewidth.Iftheareaoftherectangleis14squarecm,findthelengthandthewidth.